It is generally accepted that the interpretation and use of logging data obtained from carbonate reservoirs pose significant technical and scientific challenges. Most methods introduced for siliciclastic formations are inadequate for predicting the producibility of carbonate formations due to the complexity of their texture and pore structures and their distribution. Carbonate rock are much more than sandstones subject to a process termed diagenesis. Diagenesis alters the pore size and distribution through a number of geochemical reactions, such as chemical dissolution and reprecipitation, dolomitization, and fracturing. The shape and size of the pore network in carbonate rock is often heterogeneous even on a small scale.
Using logging measurements to derive an accurate estimate of important formation parameters, such as saturation and recovery rates, is in principle a well established procedure. However many of the predictions and estimates based on known methods depend on using fixed values for unknowns in mathematical relations which link directly measureable well logging parameters to those of interest for predicting the future production of hydrocarbons. Among the most important of these relations used in the oilfield are a group of equation in general referred to “Archie's Laws”.
Archie's laws link water saturation of a formation to its measureable resistivity. They are usually presented in a form such asR=a*Rw/(φ**m)*(S**n),  [1]in which R is the resistivity as measured in log measurements, a is a formation factor set usually to 1 in the absence of any other data, Rw the resistivity of water in the formation, φ is the porosity as measured from density, neutron or sonic logging tools or magnetic resonance or NMR logging tools and S is the water saturation within the measured volume. The two exponents m and n in equation [1] are collectively known as Archie's exponents or, respectively, as cementation exponent and saturation exponent. The saturation exponent n varies widely depending on the wettability of the formation and is usually assumed to be in the range between 1.6 and 8. The cementation exponent m is taken to be around 2. However these values are typically the result of core tests performed in the laboratory and extrapolated to downhole formations of similar type and locations.
It is the ultimate goal of equations such as equation [1] to determine the oil or water saturation of the formation unperturbed by the invasion of drilling fluid as used in the drilling of the logged well. These saturations together with an estimate of the recoverable part of the oil saturation ultimately determine the economic viability of any field development and production planning. As can be seen from the structure of Archie's laws, minor variations in the value of m and n have a significant impact on the estimate of the water saturation. And whilst tools and methods for measuring the resistivity R and the porosity φ have greatly improved over time, the determination of the exponents has been mainly left to evaluating plausible physical models for the conductivity of porous media.
As the result of such modeling, several relations have been proposed to link the cementation exponent m to measureable parameters. Some of these relations are listed below as equations [2]-[5]:m=0.019/φ+1.87,  [2]m=(2*log φ(s))/(log φ(t)),  [3]m=2.05−φ, and  [4]m=2.2−0.035/(φ+0.042).  [5]Wherein φ denotes the porosity in general, φ(s) the porosity measured by a sonic tool and φ(t) the total porosity as determined for example from nuclear porosity logs.
A further derivation of the parameter m based on the evaluation of log measurements is described by M. Wafta et al. in SPE 15714 (1987). The authors use the output of an Electromagnetic Propagation Tool (EPT) and the resistivity of invaded zones (Rxo) as the main input for estimating m. A method to calculate m, n, and a simultaneously when saturation, effective porosity, and resistivity of the sample or zone are available is published by S. M Frailey et al in: “Simultaneous Calculation of Archie Parameters m, n, and a”, West Texas Geologic Society Fall Symposium, Proceedings, October 2002, Midland, Tex. (http://www.depts.ttu.edu/peWeb/research/caprs/caprsPapers/ArchieParameters. pdf).
The above examples can only be representative of a very large body of published literature on what is a very active area of investigation in the oilfield industry.
In the view of the above prior art it is seen as an object of the present invention to provide methods for determining reservoir parameters and in particular improved methods for determining the cementation factor or porosity exponent or any mathematically equivalent term.